On the geometry of sub-Riemannian manifolds equipped with a canonical quarter-symmetric connection
Дифференциальная геометрия многообразий фигур, 2023 In this article, a sub-Riemannian manifold of contact type is understood as a Riemannian manifold equipped with a regular distribution of codimension-one and by a unit structure vector field orthogonal to this distribution. This vector field is called a
S. V. Galaev
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Anisotropically Weighted and Nonholonomically Constrained Evolutions on Manifolds
Entropy, 2016 We present evolution equations for a family of paths that results from anisotropically weighting curve energies in non-linear statistics of manifold valued data. This situation arises when performing inference on data that have non-trivial covariance and
Stefan Sommer
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Model spaces in sub-Riemannian geometry [PDF]
Communications in Analysis and Geometry, 2021 25 pages.
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Sub-Riemannian geometry, Hamiltonian dynamics, micro-swimmers, copepod nauplii and copepod robot
Pacific Journal of Mathematics for Industry, 2018 The objective of this article is to present the seminal concepts and techniques of Sub-Riemannian geometry and Hamiltonian dynamics, complemented by adapted software to analyze the dynamics of the copepod micro-swimmer, where the model of swimming is the
Bernard Bonnard +3 more
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A Comprehensive Introduction to Sub-Riemannian Geometry [PDF]
, 2019 Sub-Riemannian geometry is the geometry of a world with nonholonomic constraints. In such a world, one can move, send and receive information only in certain admissible directions but eventually can reach every position from any other. In the last two decades sub-Riemannian geometry has emerged as an independent research domain impacting on several ...
Agrachev, Andrei +2 more
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On geometry of sub-Riemannian η-Einstein manifolds
Дифференциальная геометрия многообразий фигур, 2019 On a sub-Riemannian manifold of contact type a connection with torsion is considered, called in the work a Ψ-connection. A Ψ-connection is a particular case of an N-connection.
S. Galaev
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On 4-dimensional Einsteinian manifolds with parallel null distribution [PDF]
ریاضی و جامعه, 2023 In this paper, we investigate the Einsteinian manifolds with parallel null distribution. For this purpose, we first obtain the equations, which are known as Einstein's equations, that lead to finding the mentioned manifolds and then, we reduce Einstein's
Mehdi Jafari
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Nilpotent Approximations of Sub-Riemannian Distances for Fast Perceptual Grouping of Blood Vessels in 2D and 3D [PDF]
, 2017 We propose an efficient approach for the grouping of local orientations (points on vessels) via nilpotent approximations of sub-Riemannian distances in the 2D and 3D roto-translation groups $SE(2)$ and $SE(3)$.
Bekkers, Erik J. +2 more
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A right-invariant sub-Riemannian setting for Large Deformation models [PDF]
ESAIM: Proceedings and SurveysThe Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework introduced in [BMTY05, Tro95, DGM98] is a widely recognized method in shape analysis and computational anatomy.
Pierron Thomas
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The left-invariant contact metric structure on the Sol manifold
Учёные записки Казанского университета: Серия Физико-математические науки, 2020 Among the known eight-dimensional Thurston geometries, there is a geometry of the Sol manifold – a Lie group consisting of real special matrices. For a left-invariant Riemannian metric on the Sol manifold, the left shift group is a maximal simple ...
V.I. Pan’zhenskii, A.O. Rastrepina
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